Anticipating synchrony in dynamical systems using information theory

Abstract

Synchronization in coupled dynamical systems has been a well-known phenomenon in the field of nonlinear dynamics for a long time. This phenomenon has been investigated extensively both analytically and experimentally. Although synchronization is observed in different areas of our real life, in some cases, this phenomenon is harmful; consequently, an early warning of synchronization becomes an unavoidable requirement. This paper focuses on this issue and proposes a reliable measure ([Formula: see text]), from the perspective of the information theory, to detect complete and generalized synchronizations early in the context of interacting oscillators. The proposed measure [Formula: see text] is an explicit function of the joint entropy and mutual information of the coupled oscillators. The applicability of [Formula: see text] to anticipate generalized and complete synchronizations is justified using numerical analysis of mathematical models and experimental data. Mathematical models involve the interaction of two low-dimensional, autonomous, chaotic oscillators and a network of coupled Rössler and van der Pol oscillators. The experimental data are generated from laboratory-scale turbulent thermoacoustic systems.